Methods and apparatus for sensing touch events on a display

ABSTRACT

Methods and apparatus provide for a touch sensitive display, in which a transparent layer is disposed over a display layer; light is directed to propagate into and/or through the transparent layer; scattered light is measured in response to an object touching a surface the transparent layer and disturbing the propagation of the light therethrough; and one or more positions at which the object touches the transparent layer are computed based on signals obtained by the step of measuring the scattered light.

BACKGROUND OF THE INVENTION

The present invention relates to methods and apparatus for sensing touchevents on a touch sensitive display, such as a liquid crystal display,organic light emitting diode display, etc.

The display market is prime for displays that offer touch sensingcapability—and the market size for displays with touch functionality isexpected to grow tremendously in the coming years. As a result, manycompanies have researched a variety of sensing techniques, includingresistive, projected capacitive, infrared, etc. While many of thesetechniques result in reasonable touch capability, each technique carriessome performance disadvantage for specific applications, and nearly allresult in significant added cost to the manufacture of each display.

In terms of performance, the basic metrics for touch sensitive displaysare the accurate sensing of a touch event and the determination of theprecise location of the touch event on the touch/display window. Manysecondary attributes are becoming important for added functionality,including flexibility in sensing various touching implements beyond thehuman finger, such as a pen, stylus, etc., the ability to sensemultiple, simultaneous touch events, location resolution, and theability to distinguish false touches (hovering, or environmentaldisturbances).

As touch sensitive displays are gaining wider use in mobile deviceapplications, such as the iPhone™, iPOD™, etc., the overall thicknessand weight of the touch sensitive display are becoming more importantmetrics for commercial viability. When such additional criteria aretaken into consideration, very few sensor technologies stand out.

Currently, resistive touch-screens dominate the market because of theirscalability and relatively low cost. A common variety of resistivetouch-screen is the 4-wire type, where two un-patterned transparentconductors (typically coatings of Indium tin oxide, ITO) face oneanother, one on the underside of a plastic film and the other atop aglass substrate. Voltage is alternately applied to each conductor onopposing edges. Due to resistance within the conductors, a voltage dropsacross the sheet. When voltage is not applied to a given sheet, thatsheet acts as a sensor. When the plastic film is displaced via a touchevent, the two conductive sheets come in contact with one another andcurrent flows from the energized sheet to the non-energized sheet. Thevoltage at the point of contact depends upon the distance from the inputsource, which allows the position of the contact to be determined in onedimension. By reversing the source and sense roles of the two sheets,the position can be similarly determined in the other dimension.

There are number of disadvantages associated with resistivetouch-screens, such as the plastic film being relatively prone todamage, the ITO coating being prone to cracking (as such coating isfairly brittle), and the ITO coating neither being as transparent norconductive as desirable. Resistive touch-screens are also unable tosupport multi-touch capability first popularized in the iPhone™ (whichuses a capacitive touch-screen). The very light touch possible on theiPhone is also not possible on a resistive touch-screen because the filmmust be physically displaced to bring the two ITO coatings into contact.

Although more costly than the resistive variety, capacitivetouch-screens are becoming more popular. A capacitive touch-screenincludes a touch glass layer and a cover glass layer. The touch glasslayer carries electrical traces (usually ITO) on opposing sides, usuallyin a crossing grid pattern with an insulator (the glass) therebetween.As the human body is a conductor, touching the cover glass results in adistortion of the local electrostatic field, measurable as a change incapacitance. A square wave is sequentially input into each electricaltrace in a given direction, and the mutual capacitive coupling to eachof the lines in the other direction is sensed. If a finger touches thecover glass, the mutual capacitance will be reduced at more than oneunit cell (the crossing of respective traces of the grid). Capacitivetouch-screens are desirable due to their ability to provide multi-touchsensitivity, their ability to sense even very light touch events, theirrobustness (no flexing is required), and their transparencycharacteristics.

The drawbacks of capacitive touch-screen technology include: theinability to sense the touch of a stylus, the difficulty in scaling tolarger sizes, and the high cost of manufacture.

Accordingly, there are needs in the art for new methods and apparatusfor advancing touch-screen technology to include: good scalability, lowcost, sensitivity to a stylus, robustness, good transparency,sensitivity to multi-touch events, and sensitivity to light touchevents.

SUMMARY OF THE INVENTION

In accordance with one or more embodiments described herein, methods andapparatus provide for a touch sensitive display, which may include: adisplay layer; a transparent layer disposed over the display layer; atleast one source directing light to propagate into and/or through thetransparent layer; at least one light sensing element in communicationwith the transparent layer and operating to receive scattered light inresponse to an object touching a surface the transparent layer anddisturbing the propagation of the light therethrough; and a controlcircuit including a processor receiving signals from the at least onelight sensing element indicative of the scattered light, and computingone or more positions at which the object touches the transparent layer.

A method in accordance with one or more embodiments described herein mayinclude: disposing a transparent layer over a display layer; directinglight to propagate into and/or through the transparent layer; measuringscattered light in response to an object touching a surface thetransparent layer and disturbing the propagation of the lighttherethrough; and computing one or more positions at which the objecttouches the transparent layer based on signals obtained by the step ofmeasuring the scattered light.

Other aspects, features, and advantages of the embodiments herein willbe apparent to one skilled in the art from the description herein takenin conjunction with the accompanying drawings.

DESCRIPTION OF THE DRAWINGS

For the purposes of illustration, there are forms shown in the drawingsthat are presently preferred, it being understood, however, that theembodiments described herein are not limited to the precise arrangementsand instrumentalities shown.

FIG. 1 is a side view of a touch sensitive display having certaincharacteristics that may be employed in one or more embodiments herein;

FIGS. 2A-2B are side views of touch sensitive displays employing lightreflection reduction mechanisms in accordance with one or moreembodiments herein;

FIG. 3 is a schematic view of an alternative implementation of a touchsensitive display in accordance with one or more further embodimentsherein;

FIG. 4 is a side view of a touch sensitive display employing a furtherlight reflection reduction mechanism in accordance with one or moreembodiments herein;

FIG. 5 is a graph illustrating some transmission characteristics of oneor more filters used in the light reflection reduction mechanism of FIG.5;

FIG. 6 is a schematic view of a further alternative implementation of atouch sensitive display in accordance with one or more still furtherembodiments herein;

FIG. 7 is a schematic view of an active stylus that may be used inaccordance with one or more still further embodiments herein;

FIG. 8 is a side view of an alternative touch sensitive display inaccordance with one or more further embodiments herein; and

FIG. 9 is a block diagram of a code modulator and demodulator circuitsuitable for use with one or more of the embodiments herein.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

With reference to the drawings wherein like numerals indicate likeelements there is shown in FIG. 1 a touch sensitive display 100A inaccordance with one or more embodiments and aspects described herein.The touch sensitive display 100A may be used in a variety of consumerelectronic articles, for example, cell-phones and other electronicdevices capable of wireless communication, music players, notebookcomputers, mobile devices, game controllers, computer “mice”, electronicbook readers and other devices.

The touch sensitive display 100A includes a display layer 102 and atouch screen layer 104 (which may also operate as a protective coverlayer). The touch sensitive display 100A may include an air gap betweenthe display layer 102 and the touch glass 104.

The touch screen layer 104 includes a surface 106 which is available toa user to interact with the touch sensitive display 100A through touchevents. Various indicia or indicium may be presented to the user on orthrough the surface 106 in order to guide the user in suchinteractivity. By way of example, the indicium may include areas on thesurface 106 of the screen 104 that are set aside for indicating userchoices, software execution, etc., just to name a few. As will bediscussed in further detail later in this description, the touchsensitive display 100A may include electronic circuitry that receivessignals from the screen 104 in order to detect the touching events,including the specific locations of the events on the surface 106.

The touch screen layer 104 may be formed from any suitable transparentmaterial, such as glass, plastic, or the like. While plastic is lessexpensive, glass is believed to lead to better performance. Thus, theremainder of this description will assume that a glass material is usedto form the touch screen layer 104. By way of example, the glass may bea chemically strengthened glass, such as a soda-lime type glass. Onesuch glass is an alkali aluminosilicate glass hardened through ionexchange. These types of glasses are frequently compositions consisting,not only of Na₂O (soda), CaO (lime) and SiO₂ (silica), but also ofseveral other oxides such as MgO, Li₂O, K₂O, ZnO, and ZrO₂. Oncehardened through ion exchange, these types of glass exhibit certaincharacteristics that make them desirable not only for touch screenapplications, but also for cover glass (protective) applications.Further details as to the formulation and/or production details ofsoda-lime type glass suitable for use as the touch screen 104 may befound in one or more of: U.S. patent application Ser. No. 11/888,213filed Jul. 31, 2007; U.S. patent application Ser. No. 12/537,393 filedAug. 7, 2009; U.S. patent application Ser. No. 12/545,475 filed Aug. 21,2009; and U.S. patent application Ser. No. 12/392,577 filed Feb. 25,2009, the entire disclosures of which are hereby incorporated byreference.

The display layer 102 may be implemented using any of the knownelectronic display technologies, such as LCD display technology, etc.The display may include a backlighting mechanism (not shown) thatproduces and transmits light through the touch glass layer 104,generally perpendicularly through the surface 106 as illustrated by thedashed arrows. In one or more embodiments, the aforementioned indiciummay be presented to the user by way of the display layer 102 projectinglight through the touch screen layer 104.

Whether via the backlighting mechanism or another source of light 110,the touch sensitive display 100A includes at least one source directinglight to propagate into and/or through the glass layer. In the case ofthe backlighting mechanism of the display layer 102, the light therefromwould propagate through the touch glass layer 104, generallyperpendicularly. In the case of the light source 110, the lighttherefrom would couple into the touch glass layer 104 through the edgethereof and propagate within the glass in a guided mode 112. By way ofexample, the light source 110 may include one or more LEDs, such asvisible light LEDs that emit light in the wavelength range of about 400nm to about 650 nm, or infrared LEDs that emit light at wavelengths inexcess of about 700 nm.

When an object, such as a user's finger, touches the surface 106 of thetouch glass layer 104 the propagation of the light therethrough isdisturbed, thereby creating scattered light energy 114. The touchsensitive display 100A includes at least one light sensing element 116in communication with the glass layer 104 and operating to receive orsense the scattered light energy 114 in response to the object touchingthe surface 106. The at least one light sensing element 116 (such as aphotodiode, imager, or similar device) may produce signals indicative ofthe scattered light energy 114 sufficient to compute one or morepositions at which the object touches the glass layer 104. Methods ofcomputing the positions of touch events will be discussed in more detaillater in this description.

In order to maintain good signal to noise ratios for accurate sensing ofthe scattered light 114 by the light sensing element 116, it isdesirable to minimize reflections of the in-coupled light 112 and/or thescattered light 114 off of the edge surfaces of the touch glass layer104. In this regard, and with reference to FIGS. 2A and 2B, the touchsensitive display 100A (and/or any of the other embodiments herein) mayfurther include one or more light suppressing mechanisms 120A and/or120B, which operate to reduce such light reflections.

The light suppressing mechanism 120A includes a low reflectance pigment(such as black paint or light absorbing material) disposed along atleast one edge of the glass layer 104. When at least one source 110 isemployed to in-couple the light 112, then it is desirable to have thelow reflectance pigment of the light suppressing mechanism 120A disposedon an opposite edge from the source 110. The low reflectance pigment mayperform well when applied only to the edge surface itself; however, itis believe that advantageous results are obtained when the pigment isdisposed on the edge surface as well as on at least a portion of theupper and lower surfaces of the glass 104 adjacent such edge. It may bebest to include the pigment on all edge surfaces of the glass layer 104as well as the associated portions of the adjacent surfaces.

The light suppressing mechanism 120B includes a tapering thickness ofthe glass layer 104 at the edge or edges. Again, when at least onesource 110 is employed to in-couple the light 112, then it is desirableto have the tapering edge of the light suppressing mechanism 120Bdisposed on an opposite edge from the source 110. Further, it may belikewise desirable to employ the light suppressing mechanism 120B on alledges of the glass layer 104. The taper of the light suppressingmechanism 120B imparts a “leaky-waveguide” characteristic to the touchglass layer 104 in order to suppress light reflections back into theglass. In essence, the taper of the light suppressing mechanism 120Breduces the backscattering by allowing light reaching the edge of theglass layer 104 to leak out.

To illustrate the functionality of the leaky-waveguide characteristic,FIG. 2B illustrates two guided rays within the touch glass layer 104.The first ray 122 is at about 40 degrees with respect to normal of thesurface 106, which is near the critical angle of about 39.5 degrees fora glass with a refractive index about 1.572. The second ray 124propagates down the center of the touch glass layer 104 before strikingthe tapered region. These two rays 122, 124 represent the extreme rangeof guided wave ray angles. As the rays 122, 124 strike, reflect, andre-strike the tapered portion of the light suppressing mechanism 120B,the angle of incidence changes until they are incident below thecritical angle and begin to leak out of the touch glass layer 104. Inthis way, reflectance back into the touch glass layer 104 is reducedand/or minimized.

The quality of the suppression of the backscattering (e.g., the numberof bounces and return loss) will depend on the geometry and therefractive index of the touch glass layer 104. It has been estimated viacalculation that, for a glass with a refractive index of about 1.572, athickness of 1 unit, and a taper of 10 degrees (e.g., tapering for about5.59 units), the rays 122, 124 will experience approximately 7 leakybounces. Although a taper of 10 degrees has been considered anddisclosed, other taper angles may be employed. Generally, the shallowerthe taper, the more leaky bounces the rays 122, 124 will encounterbefore reflecting back into the touch glass layer 104. Furthercalculations as to the ray 122 revealed a return loss (due to the sevenleaky bounces) of about 6.65E-13 for p-polarized light, and 3.01E-9 fors-polarization. The reflected light is strongly s-polarized. Since anLED source 110 is randomly polarized, the average edge reflection isabout 1.5E-9. Further suppression of the reflection (two or three ordersof magnitude) can be achieved by placing a p-transmitting polarizer infront of the light sensing element 116. In addition, employing theaforementioned pigment (such as black paint or light absorbing material)on the taper may also reduce the edge reflection.

Reference is now made to FIG. 3, which illustrates a schematic of analternative implementation of a touch sensitive display 100B inaccordance with one or more further embodiments herein. The touchsensitive display 100B includes a display layer (not shown) and a touchglass layer 104, which is shown from a top view, and which again mayalso operate as a protective cover glass layer. In this embodiment, thetouch sensitive display 100B includes a plurality of sources of light110A, 110B, 110C, and 110D, where each source 110 is in communicationwith a respective one of the edges 130A, 130B, 130D, and 130D of thescreen 104. As will be discussed in more detail below, employing atleast one source 110 at each edge 130 of the screen 104 providesadvantageous functionality as opposed to lesser numbers of sources 110.Nevertheless, although four such sources 110 are shown, any reasonablenumber may be used. For example, two, three or more such sources 110 maybe employed.

The touch sensitive display 100B includes a plurality of light sensingelements 116A, 116B, 116C, and 116D, each located strategically about aperiphery of the screen. In particular, advantageous operation may beachieved when a respective one of the light sensing elements 116 islocated at each corner of the screen 104. It is understood, however,that any number of light sensing elements 116 may be employed, and anylocation(s) thereof may be used, so long as sufficient sensingcapability is achieved.

The touch sensitive display 100B also includes, or is coupled to, acontrol circuit 140. The control circuit 140 provides the functionalitynecessary for energizing the sources 110, receiving signals from thelight sensing elements 116, and processing such signals to determine theone or more positions at which the object touches the surface 106 of thetouch glass layer 104. In particular, the control circuit includes amicroprocessor 142, a driver circuit 144, and an interface circuit 146.The microprocessor 142 is coupled to the driver circuit 144 and theinterface circuit 146 via signal lines, buses, or the like. Themicroprocessor 142 executes computer readable code (software programs)that controls and orchestrates the activities of the driver circuit 144and the interface circuit 146 to achieve the aforementioned functions.For example, the microprocessor 142 may provide control signals to thedriver circuit 144 indicating when to turn on and turn off therespective sources 110. As will be discussed in more detail laterherein, the microprocessor 142 may also provide additional informationsuch that the driver circuit 144 modulates the light emitted from thesources 110. The interface circuit 146 receives signals from the lightsensitive elements 116 and processes such signals so that they may beinput into the microprocessor 142. For example, when the light sensitiveelements 116 are photodiodes, the interface circuit 146 may provideappropriate biasing conditions to the photodiodes such that they areable to properly sense light energy. In this regard, the interfacecircuit 146 may cause certain light sensing elements 116 to be activeand others inactive during particular intervals of time. The interfacecircuit 146 may also process analog signals received from thephotodiodes and convert same to a digital format for the microprocessor142.

The microprocessor 142 may be implemented utilizing suitable hardware,such as standard digital circuitry, any of the known processors that areoperable to execute software and/or firmware programs, one or moreprogrammable digital devices or systems, such as programmable read onlymemories (PROMs), programmable array logic devices (PALs), etc.Furthermore, although the control circuit 140 is shown as beingpartitioned into certain functional blocks (the microprocessor 142, thedriver 144, and the interface 146), such blocks may be implemented byway of separate circuitry and/or combined into one or more functionalunits.

The microprocessor 142 may execute different software programs to carryout different techniques for computing the one or more positions atwhich the object touches the surface 106 of the touch glass layer 104.One such technique is triangulation, which is a well known process fordetermining the location of a variable point (in this case the point(s)at which the object touches to screen 104) by measuring angles to suchpoint from known points. The variable point can then be computed as thethird point of a triangle with one known side and two known angles. Inthe touch sensitive display 100B, any two of the light sensitiveelements 116 may provide the fixed points in the triangulationalgorithm. In order to improve the accuracy of the position calculation,it may be desirable to use multiple pairs of the light sensitiveelements 116 to compute the touch point a plurality of times and thenusing statistical computations to arrive at a final touch location.

In some embodiments, the operational characteristics of the lightsensitive elements 116 may make the use of triangulation problematic.For example, if the light sensitive elements 116 are photodiodes, whichonly measure light intensity, then triangulation may be difficult orimpossible. An alternative approach to computing the position of a touchevent is to compare the respective signal strengths sensed by the lightsensitive elements 116. By way of example, if elements 116A and 116Dmeasure the same signal strength, then it may be determined that theposition of the touch event lies on a line equidistant from the twoelements 116A and 116D. If the signals are not equal, however, then theposition of the touch event may be determined to be closer to oneelement than the other. Indeed, the position of the touch event wouldnot lie on a line, but rather on an arc. By sensing the signal strengthof a third element 116B, a determination of a single point for the touchposition may be achieved. For purposes of illustration and notlimitation, an exemplary algorithm for computing the position of touchevents on the screen 104 based on amplitude data received from the lightsensing elements 116 is discussed later in this description under theheading of “EXAMPLE—POSITION SENSING ALGORITHM”.

Among the factors influencing the accuracy of the mathematical techniqueused to compute the touch location is the ability of the microprocessor142 to distinguish among the signals received from the light sensingelements 116 as resulting from light energy from a particular lightsource 110 or set of light sources 110. In this regard, the controlcircuit 140 is operable to cause the light emanating from at least two(and preferably all) of the sources 110 to include at least onedistinguishing characteristic. In this way, the microprocessor 142 mayextract an indication of such characteristic from the signals producedby the light sensitive elements 116 and, thus, distinguish which of thesignals are from scattered light produced in response to particular onesof the sources 110.

The distinguishing characteristics may include at least one of: (i) adiffering wavelength of the light emanating from two or more of thesources 110; (ii) a modulation component whereby the light emanatingfrom two or more is modulated with respective, differing codes; and(iii) a frequency modulation component whereby the light emanating fromtwo or more sources is modulated with respective, differing frequencies,and (iv) a temporal component (or time multiplexing) whereby lightemanates from two or more of the sources at differing times.

Taking each of the above distinguishing characteristics in turn, each ofthe sources 110 may be implemented with a respective LED of differinglight wavelength. For example, the source 110A may emit light within afirst range of wavelengths, such as between about 430 nm and about 470nm (which is generally the blue light spectrum). The source 110B mayemit light within a second range of wavelengths, such as between about490 nm and about 550 nm (which is generally the green light spectrum).The source 110C may emit light within a third range of wavelengths, suchas between about 615 nm and about 650 nm (which is generally the redlight spectrum). These visible blue, green, and red ranges ofwavelengths are for illustration purposes only. Indeed, other ranges(including composite blue-green, green-red, etc.) are also possible.Further, non-visible wavelengths may also be employed, such as infra-redwavelengths. Thus, for example, the source 110D may emit light within afourth range of wavelengths, such as between about 820 nm and about 880nm.

Given that two or more of the sources 110 may be emitting light atdifferent wavelengths, steps may be taken within the screen 104 itselfand/or the control circuit 140 to distinguish among the signals receivedfrom the light sensing elements 116. For example, the light sensingelements 116 may be positioned in ways that would tend to cause onlycertain elements 116 to sense scattered light originating from certainsources 110. In particular, given the orientation of the light sensingelements 116, the light projection field of each source 110 may excludecertain of the light sensing elements 116. By way of example, the lightprojection field of the source 110A may include portions of the screen104 only forward of dashed lines 134A. Assuming that light reflectionsat the edges 130 of the screen 104 are reduced or minimized, only lightsensing elements 116A and 116D (along the same edge 130A as source 110A)would receive scattered light energy from a touch event originatingfrom, and no light energy directly incident from, the source 110A.Similar analysis would apply to the other sources 110 and light sensingelements 116.

The light sensing elements 116 themselves may be responsive to thewavelength of light energy in different ways as is known in the art. Forexample, a given light sensing element 116 may include sensorsresponsive to some wavelengths and not others, thereby providing anoutput indicative of not only the magnitude of the light energyreceived, but also as to the wavelength(s) thereof.

The control circuit 140, and the microprocessor 142 in particular, candistinguish among the signals received from the respective light sensingelements 116 as being from light scattering events as opposed toincident light from the sources 110. Further, such signals may be usedin a mathematical algorithm suitable for computing the location orlocations of touch events on the screen 104.

As discussed above, the accuracy of the touch position calculation usingthe distinguishing characteristic of wavelength (as well as one or moreother characteristics to be discussed below) is influenced by the extentand character of light reflections at the edges 130 of the screen 104.It is most desirable that such edge reflections are reduced orminimized. In this regard, the touch sensitive display 100B may includeadditional features to reduce such edge reflections beyond or inaddition to those previously discussed with respect to FIGS. 2A-2B.

In this regard, reference is made to FIG. 4, which illustrates a sideview of the touch glass layer 104 employing a further light reflectionreduction mechanism. In particular, the low reflectance pigment 120A maybe disposed along an edge 130 (preferably all edges) of the glass layer104. The low reflectance pigment 120A may include a respective windowtherethrough adjacent the respective sources 110 such that the lighttherefrom is coupled unimpeded into the glass layer 104. In order toreduce reflections from the window and/or the source 110 itself (arisingfrom light energy incident from another source or scattering event) atleast one filter 126 may be disposed between the source 110 and the edge130 of the glass layer 104. The filter 126 operates to attenuate lightsubstantially outside the range of wavelengths produced by therespective source 110. In this way, the window and the source 110 itselfwill appear “dark” (i.e., non-reflective) to light outside such range ofwavelengths. In the case of visible wavelength ranges, it is possible toemploy a single filter 126, depending on the particular filtercharacteristics thereof. However, in some cases first and second filters126A, 126B may be required to filter the entire range of interest. Forexample, one filter 126A may attenuate light outside a first range ofvisible wavelengths (such as the aforementioned blue light range), whileanother filter 126B may attenuate light outside another such range, suchas the infrared range of wavelengths.

FIG. 5 is a graph illustrating some transmission characteristics of oneor more of the filters 126. In particular, relationships between theincident light wavelengths (e.g., blue 128A, green 128B, red 128C,infra-red 128D) and the respective filter characteristics 129A, 129B,129C, 129D are shown. The vertical axis of the graph is percenttransmission of the source 110 or through the filter 126 as the case maybe, while the horizontal axis is light wavelength in units of nm.

If it is determined that the aforementioned pigment, taper, and/orfilers 126 do not attenuate the edge reflections sufficiently, thenfurther discrimination of desired signals versus undesired signals fromthe light sensing elements 116 may be obtained by modulating the lightproduced by the sources 110 with some additional information. By way ofexample, the driver circuit 144 may modulate one or more of the sources110 such that the respective light therefrom includes a certain code orcodes, such as orthogonal codes, like well known Walsh codes. By way ofexample, the light produced by a particular source 110 may include amodulated 20 bit Walsh code at a particular bit rate (such as 1 KHz).The interface circuit 146 may include a receiver that can demodulate theparticular Walsh code and reject signals that do not include such code.This modulation/demodulation process ensures that only signals producedin response to scattered light from a touch event (as opposed to lightemitted directly by other sources 110 on an opposing or adjacent edge)are processed to compute the touch location. It is noted that modulatorand demodulator circuits (such as for orthogonal coding schemes) arewell known in the signal processing arts. For the purposes ofdiscussion, a more detailed description of an implementation of suchmodulator and demodulator circuits is presented later in thisdescription under the heading “EXAMPLE—CODE MODULATION IMPLEMENTATION”.

A variant of the above code modulation is the use of frequencymodulation. In this embodiment, the driver circuit 144 may modulate oneor more of the sources 110 such that the respective light therefromincludes a certain frequency or frequencies (which may be distinguishedby a tuned receiver). The interface circuit 146 may include a suitablereceiver that can demodulate the particular frequency and reject signalsthat do not include such frequency. As with code modulation, thismodulation/demodulation process ensures that only signals produced inresponse to scattered light from a touch event (as opposed to lightemitted directly by sources 110 on an opposing or adjacent edge) areprocessed to compute the touch location. It is noted that frequencymodulator and demodulator circuits are well known in the signalprocessing arts and, therefore, a detailed description ofimplementations thereof are omitted from this description.

Now, taking the next of the distinguishing characteristic that may beemployed to assist in isolating the signals carrying information as toparticular scattering events and particular light sensing elements 116,each of the sources 110 may be energized in a time multiplexing fashion.For example, the control circuit 140 (e.g., the driver circuit 144) maycause only one (or particular ones) of the sources 110 to emit lightduring a particular time interval. Concurrently, the control circuit 140(e.g., the interface circuit 146) may permit only certain ones of thelight sensing elements 116 to be active during such time interval.

To illustrate the above, when source 110A is active, the control circuit140 may only activate light sensing elements 116A and 116D. Under theseconditions, and assuming limited edge reflections, only light sensingelements 116A and 116D (along the same edge 130A as source 110A) wouldreceive scattered light energy from a touch event originating from, andno light energy directly incident from, the source 110A. Similaranalysis would apply to the other sources 110 and light sensing elements116 during other time intervals. It is noted that this time multiplexingapproach may be employed by energizing more than one source 110 at atime, although care must then be taken to account for multiple sourcesin the computation of the touch position. Further, the time multiplexingapproach may be employed with sources 110 of the same wavelength orrange of wavelengths, since the number of sources 110 and light sensingelements 116 active at one time is limited. Thus, in order to reduce theimpact of smudges on the surface 106 of the touch screen 104, and/orpermit indicium to be actually painted on, or otherwise obstructing,such surface 106, the sources may be all of the infra-red variety.

Using the time multiplexing approach, the control circuit 140 candistinguish among the signals received from the respective light sensingelements 116 as being from light scattering events as opposed toincident light from the sources 110. This permits such signals to beused in, for example, the algorithm to compute the location or locationsof touch events on the screen 104. Again, the exemplary algorithmdiscussed under the heading of “EXAMPLE—POSITION SENSING ALGORITHM” maybe employed for computing the positions of the touch events.

Reference is now made to FIG. 6, which illustrates a schematic of analternative implementation of a touch sensitive display 100C inaccordance with one or more further embodiments herein. The touchsensitive display 100C also includes a display layer (not shown) and atouch glass layer 104, which is shown from a top view. In thisembodiment, the touch sensitive display 100C includes a plurality ofsources of light 110A (such as four) along the one edge 130A, aplurality of sources of light 110B along another edge 130B, etc.Similarly, the touch sensitive display 100C includes a plurality oflight sensing elements (such as four) along the edge 130A, a pluralityof light sensing elements along the other edge 130B, etc. As with otherembodiments herein, the touch sensitive display 100C also includes, oris coupled to a control circuit 140. The touch sensitive display 100Cmay operate in similar ways as the touch sensitive display 100B of theprior embodiments, however, all the sources 110 along a given edge 130of the screen 104 may be of the same wavelength (or range thereof) inthe case of wavelength division multiplexing, and/or beactivated/deactivate at the same time, in the case of time divisionmultiplexing. So too for the light sensing elements 116 along eachrespective edge 130.

In accordance with a further alternative implementation of a touchsensitive display, any of the aforementioned implementations shown inFIGS. 1, 3, and 6 may operate on the principal of fluorescence. In theevent that the object (such as a human finger) fluoresces in response toincident light from touching the surface 106 of the glass layer 104, thefluorescent light from the object may couple into the glass layer 104.As the fluorescent light, through careful selection of the sources 110,may be of a different, higher wavelength than the incident light, thescattered light may be readily detected and detection of incident lightrejected by the control circuit 140.

As described in the current draft, a finger can backscatter lightallowing detection of a touch event. A passive stylus that couldsimilarly scatter light could do the same. But the possibility exists toprovide an active stylus. Rather than reflecting light provided in orthrough the cover glass, the active stylus would be a light source.

Reference is now made to FIG. 7, which is a schematic diagram of anactive stylus 200 that may be used in combination with one of more ofthe touch sensitive displays 100 disclosed herein. In general, theapproach of the active stylus 200 is to place the light source 210 fortouch position sensing within the housing 202 of the implement that theuser employs to touch the touch screen 104, rather than relying on lightscattering. The advantage of this approach is one of robustness sincethe light source 210 would be far stronger than any backscattered light,so strong in fact that the user could possibly rest their palm on thescreen 104 while writing with the stylus 200 without attenuating so muchlight as to preclude position detection. When using the active stylus200, the sources 110 providing light in or through the touch screen 104are not necessary, so they may be eliminated altogether or turned offtemporarily. Temporarily turning off the sources 110 would provide fordual modes of operation: one mode for touch sensitivity using thesources 110; and another mode for touch sensitivity using the activestylus 200.

The light source 210 may be an LED, such as an IR LED, in which case thelight sensing elements 116 would be adapted to sense IR light. If thelight is to be modulated as discussed above, then a means forsynchronizing the emission of light from the source 210 and the signalsdetected at the light sensing elements 116 would be employed. Such meanswould be readily apparent to a skilled artisan given the discussionabove and the system shown and described later herein with respect toFIG. 9. The light from the source shines into a ball 204 at a distal endof the housing 202, which ball 204 diffuses and randomizes the lightemitted from the stylus 200. Such diffusion eliminates the attitude ofthe stylus 200 from influencing the detection of the light from thepoint of view of the light sensing elements 116. The ball 204 may bemade of any suitable material, such as plastic that is filled with, forexample, about 1% titanium dioxide to act as the scattering agent.

It is not desirable to have the source 210 energized by the battery 206when there is no contact with the touch screen 104. There are a widevariety of potential mechanical configurations to permit the stylus 200to only turn on when in contact with the screen 104. By way of example,the ball 204 may be biased forward toward the distal end of the housing202 by way of a spring ring 208. The spring ring 208 may be made of someelastomeric material that can be compressed with relatively little forcebut springs back to its normal larger shape when pressure is released.When pressure is placed on the ball 204 and the spring ring 108 iscompressed, a conductive contact plate 212 joins two switch contacts 214allowing current to flow from the battery 206 to the source 210.Additionally or alternatively, the battery 206 may be eliminated and thestylus 200 may be able to scavenge power output by a host within thetouch sensing display 100.

FIG. 8 illustrates a further alternative touch sensitive display 110D.The touch sensitive display 100D includes a display layer 102, a glasslayer 104 (which may be disposed above the display layer 102), and aresilient touch layer 105 atop the glass layer 104. A gap is producedbetween the resilient touch layer 105 and the glass layer 104 viaspacers or the like. The touch layer 105 is formed from a suitablepolymer that may flex and contact the glass layer 104 in response to atouch event. In addition, the touch layer 105 is formed from a materialthat has good waveguiding properties. The light source 110 produceslight that is coupled into and propagates within the glass layer 104 ina guided mode. Due to total internal reflection within the glass layer104, without a touch event, no light is coupled into the touch layer 105and, therefore, no scattered light is sensed by the light sensingelements 116. Upon a touch event, the guided mode of the lightpropagating within the glass layer 104 is disrupted and some of thatlight couples into the touch layer 105. The light sensing elements 116may thus measure such light and provide signals indicative thereof to acontrol circuit (not shown). In this way the control circuit may computethe location of the touch event using similar techniques and apparatusdiscussed above.

Example Position Sensing Algorithm

This section describes a position detection algorithm that may be usedfor computing touch events in one or more of the embodiments disclosedand discussed above. In this section, we describe the position-detectionalgorithm, along with considerations related to its implementation in aprogram that manages the operation of the touch sensitive display.

By way of background, in everyday life, we often need to evaluate theprobability of random events. Examples include throwing a dice, drawinga card from a deck or estimating the noise of measurement instruments.In these cases, knowledge of a model describing the physical system (theprobability distribution) is used to make predictions about the outcome.When modeling data, we want to do just the opposite: given the knowledgeof empirical data, we want to find a model that provides a gooddescription. The way to achieve this may be found with reference toBayes' theorem, which states that

$\begin{matrix}{{P\left( {AB} \right)} = {\frac{{P(A)}{P\left( {BA} \right)}}{P(B)}.}} & (1)\end{matrix}$

Applied to the present problem of finding the model given the empiricaldata, Bayes' theorem becomes

$\begin{matrix}{{P\left( {{model}{data}} \right)} = {\frac{{P({model})}{P\left( {{data}{model}} \right)}}{P({data})}.}} & (2)\end{matrix}$

The probability P(model) is called the prior; it can be taken to be aconstant if no assumption is made about which model is likely to bevalid. The denominator is simply a normalization constant that ensuresthat the probability of all models be equal to one. Consequently, wefind that

P(model|data)∝P(data|model),  (3)

which means that the probability of a model being valid given thesupporting data is proportional to the probability of observing the datagiven that particular model. This result is the foundation of theparameter fitting method discussed herein.

The physical setup provides us with N data points (the signals measuredby the detectors 116), denoted {tilde over (f)}_(i), i=1, . . . , N,that we want to fit to a model f_(i)(a₁, . . . , a_(M)), where a_(j),j=1, . . . , M, are unknown parameters. This model is a function usuallybuilt using some physical insight about the nature of the randomprocess.

If the experimental error on each data point is normally distributedwith standard deviation σ_(i), then the probability of measuring thedata set {tilde over (f)}_(i) experimentally given that the modelpredicts the values f_(i) is given by

$\begin{matrix}{{P\left( {{data}{model}} \right)} \propto {\prod\limits_{i = 1}^{N}\; {{\exp \left\lbrack {{- \frac{1}{2}}\left( \frac{{\overset{\sim}{f}}_{i} - f_{i}}{\sigma_{i}} \right)^{2}} \right\rbrack}\Delta \; {f.}}}} & (4)\end{matrix}$

We know, per our discussion of Bayes' theorem, that Eq. (4) is also theprobability of the model being valid, given the observed data. Thereforethe most probable model is the one that maximizes Eq. (4), or,equivalently, that minimizes the negative of its logarithm,

$\begin{matrix}{\left\lbrack {\sum\limits_{i = 1}^{N}\; \frac{\left( {{\overset{\sim}{f}}_{i} - f_{i}} \right)^{2}}{2\sigma^{2}}} \right\rbrack - {N\; \log \; \Delta \; {f.}}} & (5)\end{matrix}$

Since N and Δf are constants, finding the most probable model isequivalent to minimizing the quantity

$\begin{matrix}{{\chi^{2}\left( {a_{1},\ldots \mspace{14mu},a_{M}} \right)} \equiv {\sum\limits_{i = 1}^{N}{{\frac{1}{\sigma_{i}^{2}}\left\lbrack {{\overset{\sim}{f}}_{i} - {f_{i}\left( {a_{1},\ldots \mspace{14mu},a_{M}} \right)}} \right\rbrack}^{2}.}}} & (6)\end{matrix}$

So the problem is reduced to finding the minimum of a (in general)nonlinear function in the M-dimensional parameter space. The values ofa₁, . . . , a_(M) which minimize χ² are called the “best-fit parametersor maximum likelihood estimators”.

The least-squares procedure outlined above includes making an assumptionabout a model and choosing the parameters that yield the best fitbetween the model and the data. But it does not actually guarantee thatthe model is a good representation of the random process. We need a“goodness-of-fit” criterion to decide whether the model is adequate.

This criterion is provided by the following result: if the model islinear in its parameters, then the quantity χ², when minimized, obeysthe chi-square distribution with v=N−M degrees of freedom. Consequently,the probability Q that the “true” model has a chi-square as large as χ²is given by

Q=1−P(χ² |v),  (7)

where P(χ²|v) is the incomplete gamma function,

$\begin{matrix}{{{P\left( {\chi^{2}v} \right)} = {\int_{0}^{\chi^{2}}{{p\left( {x,v} \right)}\ {x}}}},{with}} & (8) \\{{p\left( {x,v} \right)} = {\frac{1}{2^{v/2}{\Gamma \left( {v/2} \right)}}x^{{v/2} - 1}{^{{- x}/2}.}}} & (9)\end{matrix}$

The incomplete gamma function is available with most computationalsoftware; in Matlab™ it is called by the command “gammainc”. If Q isclose to one, then the model fits the data well. Conversely, if it isvery small, then the fit is not a good one. In practice, Q can be assmall as 10⁻³ before a model is rejected.

Although the chi-square distribution is strictly valid for linear modelsonly, it is usually a good approximation even for models that arenonlinear in their parameters.

We assume that the model f_(i)(a₁, . . . , a_(M)) has a nonlineardependence on the parameters a_(j). For this reason, the minimum of thechi-square must be found iteratively. Starting from some initial guess,we modify the parameters in order to decrease the value of χ². We repeatthe procedure until χ² stops decreasing.

Two regimes should be considered, depending on whether χ² is close to aminimum or away from it. Away from a minimum, its first derivative islarge, so chi-square can be decreased by taking steps down the gradient.Starting from the values of the parameters at step n, denoted by thevector a^((n)), the values at step n+1 are given by

a ^((n+1)) =a ^((n))−constant×∇χ²(a ^((n))).  (10)

The constant appearing in this equation should be small enough so as tonot miss the minimum by overshooting. Appropriate values are givenbelow.

Near a minimum, the gradient of χ² is small and consequently a quadraticlocal expansion around the minimum a_(min) is valid:

$\begin{matrix}{{\chi^{2}(a)} \approx {{\chi^{2}\left( a_{\min} \right)} + {\frac{1}{2}{\sum\limits_{k}\; {\sum\limits_{l}{\frac{\partial^{2}\chi^{2}}{{\partial a_{k}}{\partial a_{l}}}\left( {a_{k} - a_{k,\min}} \right){\left( {a_{l} - a_{l,\min}} \right).}}}}}}} & (11)\end{matrix}$

Taking derivatives with respect to a_(k), we get

$\begin{matrix}{\frac{\partial\chi^{2}}{\partial a_{k}} \approx {\sum\limits_{l}\; {\frac{\partial^{2}\chi^{2}}{{\partial a_{k}}{\partial a_{l}}}\left( {a_{l} - a_{l,\min}} \right)}}} & (12)\end{matrix}$

We introduce the notation

$\begin{matrix}{{\beta_{k} = {{- \frac{1}{2}}\frac{\partial\chi^{2}}{\partial a_{k}}}}{and}} & (13) \\{\alpha_{kl} = {\frac{1}{2}{\frac{\partial^{2}\chi^{2}}{{\partial a_{k}}{\partial a_{l}}}.}}} & (14)\end{matrix}$

Then Eq. (12) can be written as

$\begin{matrix}{\beta_{k} \approx {\sum\limits_{l}{\alpha_{kl}\left( {a_{l,\min} - a_{l}} \right)}}} & (15)\end{matrix}$

or, in matrix form,

β≈α(a_(min)−a).  (16)

Therefore, starting from the value a^((n)) at step n, an approximationto the minimum at step n+1 is given by

a ^((n+1)) =a ^((n))+α⁻¹β.  (17)

Let us elaborate on the calculation of the matrix elements β_(k) andα_(kl). From the definition Eq. (6), we have

$\begin{matrix}{{\beta_{k} = {\sum\limits_{i = 1}^{N}\; {\frac{1}{\sigma_{i}^{2}}\left( {{\overset{\sim}{f}}_{i} - f_{i}} \right)\frac{\partial f_{i}}{\partial a_{k}}}}}{and}} & (18) \\{\alpha_{kl} = {\sum\limits_{i = 1}^{N}\; {\frac{1}{\sigma_{i}^{2}}\left\lbrack {{\frac{\partial f_{i}}{\partial a_{k}}\frac{\partial f_{i}}{\partial a_{l}}} - {\left( {{\overset{\sim}{f}}_{i} - f_{i}} \right)\frac{\partial^{2}f_{i}}{{\partial a_{k}}{\partial a_{l}}}}} \right\rbrack}}} & (19)\end{matrix}$

The second term, involving the second derivative of f_(i), is oftenignored in practice because it is likely to be small compared with theterm containing the first derivatives and can actually cause theminimization algorithm to become unstable. Therefore we will use thefollowing formula to calculate the matrix elements α_(kl):

$\begin{matrix}{\alpha_{kl} = {\sum\limits_{i = 1}^{N}\; {\frac{1}{\sigma_{i}^{2}}\frac{\partial f_{i}}{\partial a_{k}}{\frac{\partial f_{i}}{\partial a_{l}}.}}}} & (20)\end{matrix}$

Equations (10) and (17) give the iteration procedure depending onwhether the chi-square is far from or close to a minimum. But how do weknow which regime we are in, and when to do the transition? A clevertrick is put forward by the Levenberg-Marquardt method. It also solvesthe problem of finding a constant to use in Eq. (10).

Suppose that we replace the matrix a by a′, obtained from α bymultiplying the diagonal elements by 1+λ, where λ is a constant whosevalue can be changed from one iteration to the next:

α^(ll)′=α_(ll)(1+λ)  (21)

α_(kl)′=α_(kl) fork≠l.  (22)

Upon replacement, Eq. (17) becomes

a ^((n+1)) =a ^((n))+(α′)⁻¹β.  (23)

The iteration formula Eq. (23) ensures the transition from the regionaway from a minimum to that close to a minimum. Indeed, if λ is verylarge, then the matrix α′ is essentially diagonal, so that Eq. (23)becomes

$\begin{matrix}{{a_{k}^{({n + 1})} = {a_{k}^{(n)} + \frac{\beta_{k}}{\alpha_{kk}\lambda}}},} & (24)\end{matrix}$

which is nothing but Eq. (10) with the stepping constant 1/(α_(kk)λ),which is small since λ is large. Conversely, when λ is very small, thenthe matrix α′ reduces to α, and Eq. (23) is identical to Eq. (17).Because it covers both regimes depending on the value of λ, Eq. (23) isused in the iterative procedure to find the minimum of chi-square.

Finally, it can be shown that once the minimum of χ² is found, α⁻¹ isthe covariance matrix of the parameters. In particular, the standarddeviations of the estimates are given by the diagonal elements of α⁻¹:

σ²(a _(j))=(α⁻¹)^(jj).  (25)

The following algorithm is used to minimize the chi-square in order tofind the best-fit parameters.

1. Start from some initial guess for the parameters

2. Calculate χ²(a₁, . . . , a_(M)).

3. Pick λ small, say λ=0.001.

4. Form the matricies α′ and β and calculate the next guess a_((n+1))using Eq. (23).

5. If χ²(a^((n+1)))≧χ²(a^((n))) decrease λ by 10 and return to step 4.(In other words, we are far from a minimum and we must follow thegradient while taking smaller steps.)

6. If χ²(a^((n+1)))<χ²(a^((n))) (i.e. we are getting close to theminimum), decrease λ by 10 and update the solution: a^((n))→a^((n+1)).Return to step 4.

7. Stop when χ² changes by less than 0.001.

Once the best-fit parameters have been found, it is always a good ideato calculate the probability Q given by Eq. (7) to make sure that thefit is a good one.

We now describe how the parameter-fitting method detailed above isemployed to identify the position of the touch event in the one or moreembodiments of the touch sensitive displays discussed above. Forpedagogical reasons, we will start by describing an over-simplifiedmodel that illustrates the workings of the algorithm, and we will showthat this technique performs better than simpler algebraic formulas.Then we will describe a more practical model.

In order to apply the general machinery described above, one shouldspecify a model for the data. This is where insight about the physicalsystem under consideration comes into play. One can include variousrefinements into the model in order to describe reality with the desiredlevel of accuracy. In this section we will start with the simplest modelpossible, one in which the amplitude reaching the detectors varies asthe inverse of the distance to the touch event. This model is reasonablebecause the amplitude of the light scattered by a finger touching thesurface into the planar waveguide decreases as hr. However, thisdescription is significantly simplified because it assumes that thesignal level is known and constant, that the light is not attenuated asit propagates through the glass, and neglects the angular dependence ofresponse of the detectors. Nevertheless, this model makes a goodstarting point in order to become familiar with the algorithm.

Therefore in this section we will assume that the response of detector iis given by

$\begin{matrix}{{f_{i} = \frac{1}{R_{i}}},} & (26)\end{matrix}$

with the distance between the touch event and the detector is

R _(i)=√{square root over ((x−x _(i))²+(y−y _(i))²)}{square root over((x−x _(i))²+(y−y _(i))²)},  (27)

Here, x and y are the unknown coordinates of the touch event, and x_(i)and y_(i) are the known positions of each detector.

The chi-square, function of the unknown parameters x and y, is given by

$\begin{matrix}{{{\chi^{2}\left( {x,y} \right)} = {\sum\limits_{i = 1}^{N}\left\lbrack \frac{{\overset{\sim}{f}}_{i} - {f_{i}\left( {x,y} \right)}}{\sigma_{i}} \right\rbrack^{2}}},} & (28)\end{matrix}$

where {tilde over (f)}{tilde over (f_(i))} are the measured signals fromeach of the N detectors.

In order to construct the matrices α and β required to minimize thechi-square, we must calculate the derivatives of f_(i):

$\begin{matrix}{\frac{\partial f_{i}}{\partial x} = {- \frac{x - x_{i}}{R_{i}^{3}}}} & (29) \\{\frac{\partial f_{i}}{\partial y} = {- {\frac{y - y_{i}}{R_{i}^{3}}.}}} & (30)\end{matrix}$

the matrix elements are obtained from Eqs. (18) and (20). We write themdown explicitly for clarity:

$\begin{matrix}{{\beta_{x} = {\sum\limits_{i = 1}^{N}{\frac{1}{\sigma_{i}^{2}}\left( {{\overset{\square}{f}}_{i} - f_{i}} \right)\frac{\partial f_{i}}{\partial x}}}},} & (31) \\{{\beta_{y} = {\sum\limits_{i = 1}^{N}{\frac{1}{\sigma_{i}^{2}}\left( {{\overset{\square}{f}}_{i} - f_{i}} \right)\frac{\partial f_{i}}{\partial y}}}},} & (32)\end{matrix}$

from which we construct

$\begin{matrix}{\beta = {\begin{bmatrix}\beta_{x} \\\beta_{y}\end{bmatrix}.}} & (33)\end{matrix}$

Similarly,

$\begin{matrix}{{\alpha_{xx} = {\sum\limits_{i = 1}^{N}{\frac{1}{\sigma_{i}^{2}}\left( \frac{\partial f_{i}}{\partial x} \right)^{2}}}},} & (34) \\{{\alpha_{xy} = {\sum\limits_{i = 1}^{N}{\frac{1}{\sigma_{i}^{2}}\frac{\partial f_{i}}{\partial x}\frac{\partial f_{i}}{\partial y}}}},} & (35) \\{{\alpha_{yx} = {\sum\limits_{i = 1}^{N}{\frac{1}{\sigma_{i}^{2}}\frac{\partial f_{i}}{\partial x}\frac{\partial f_{i}}{\partial y}}}},} & (36) \\{{\alpha_{yy} = {\sum\limits_{i = 1}^{N}{\frac{1}{\sigma_{i}^{2}}\left( \frac{\partial f_{i}}{\partial y} \right)^{2}}}},} & (37)\end{matrix}$

which are used to form the matrices

$\begin{matrix}{{\alpha = \begin{bmatrix}\alpha_{xx} & \alpha_{xy} \\\alpha_{yx} & \alpha_{yy}\end{bmatrix}}{and}} & (38) \\{\alpha^{\prime} = {\begin{bmatrix}{\alpha_{xx}\left( {1 + \lambda} \right)} & \alpha_{xy} \\\alpha_{yx} & {\alpha_{yy}\left( {1 + \lambda} \right)}\end{bmatrix}.}} & (39)\end{matrix}$

The vector containing the unknown parameters, a=[x,y]′, is then obtainediteratively following the procedure detailed in section 2.5.

Once the solution is obtained, the errors on the position is given bythe standard deviations

σ_(x) ²=(α⁻¹)_(xx)  (40)

σ_(y) ²=(α⁻¹)_(yy).  (41)

The progress of the chi-squared minimization algorithm is illustrated inFIGS. 1 and 2. The example used here is for a rectangular display withan aspect ratio of 2:1 and with 4 detectors located at the corners withcoordinates (x_(i),y_(i))=(±1,±0.5). Synthetic data was generated tosimulate touch at a position (x₀,y₀) using the formula

$\begin{matrix}{{\overset{\sim}{f}}_{i} = {\frac{1}{\sqrt{\left( {x_{0} - x_{i}} \right)^{2} + \left( {y_{0} - y_{i}} \right)^{2}}}.}} & (42)\end{matrix}$

The chi-squared minimization process was carried out using the origin(x,y)=(0,0) as an initial guess. It has been demonstrated throughmodelling that a plot of χ²(x,y) and the trajectory is followed by thealgorithm. The minimum located at (x₀,y₀) may be found after only a fewiterations.

In general, it is not possible to find algebraic expressions for theposition of the touch event in terms of the detector data. With a simple1/r model, however, algebraic expressions do exist. It is interesting tosee how the statistical approach compares with algebraic formulas inthis case.

Algebraic formulas can be obtained by writing down the expression for1/f_(i) ²:

$\begin{matrix}{\frac{1}{f_{i}^{2}} = {\left( {x - x_{i}} \right)^{2} + {\left( {y - y_{i}} \right)^{2}.}}} & (43)\end{matrix}$

Taking a pair of detectors 1 and 2 and calculating the quantity 1/f₁²−1/f₂ ² leads to

$\begin{matrix}{{\frac{1}{f_{1}^{2}} - \frac{1}{f_{2}^{2}}} = {{2\left( {x_{2} - x_{1}} \right)x} + x_{1}^{2} - x_{2}^{2} + {2\left( {y_{2} - y_{1}} \right)y} + y_{1}^{2} - {y_{2}^{2}.}}} & (44)\end{matrix}$

If we place these detectors such that x₂=−x₁ and y₂=y₁, then we canisolate the x coordinate:

$\begin{matrix}{x = {\frac{f_{1}^{- 2} - f_{2}^{- 2}}{2\left( {x_{2} - x_{1}} \right)}.}} & (45)\end{matrix}$

In a similar manner, the y coordinate can be isolated by taking twodifferent detectors placed at x₂=x₁ and y₂=y₁. Therefore, using 4detectors placed symmetrically at the corners of a rectangle of widthw_(x) and height w_(y), it is possible to extract the coordinates usingthe following formulas:

$\begin{matrix}{x = \frac{f_{1}^{- 2} - f_{2}^{- 2} + f_{3}^{- 2} - f_{4}^{- 2}}{4w_{x}}} & (46) \\{y = \frac{f_{1}^{- 2} + f_{2}^{- 2} - f_{3}^{- 2} - f_{4}^{- 2}}{4w_{y}}} & (47)\end{matrix}$

Let us put aside the fact that an algebraic solution does notnecessarily exist for a more complicated model. In the absence ofdetector noise, the algebraic formulas give the position accurately andwith very few operations. In this case there would be no need for astatistical approach. In the presence of detector noise, however, it isnot clear which method is more accurate. A numerical experiment has beencarried out to answer that question. A rectangular display withdetectors at each of the 4 corners (±1,±0.5) was assumed. Synthetic datawas generated for a given touch position (x₀,y₀), and gaussian noise wasadded to the value of each detector. Then the position of the touchevent was recovered using both the statistical chi-squared minimizationalgorithm and the algebraic formulas. This procedure was repeated 100times to obtain significant statistics. The standard deviations of the xand y coordinates obtained both ways were then calculated and compared.The entire procedure was then repeated for a different value of thetouch position (x₀,y₀).

In this example the noise added to the synthetic data was gaussian witha standard deviation of σ_(i)=0.0. The results from the accuracy studycompare the uncertainties of the recovered coordinates, σ_(x) and σ_(y),obtained with the algebraic and statistical method. (In the latter case,the standard deviations were obtained in two ways: from the analyticalformulas Eqs. (40-41), and from the many statistical realizations.)

It was determined through experimentation that the statistical methodwas more accurate than the algebraic formulas. We also found that thestandard deviations obtained from the multiple realizations were equalto those predicted theoretically, which reinforced confidence in theunderlying theory.

The poor accuracy of the algebraic approach lies in the fact that theformulas use the square of the inverse of the experimental data, f_(i)⁻². For this reason, the strong signals, which we would expect tocontain most of the information, have weak contributions. Conversely,the weak signals, which are most affected by noise, are the dominantcontribution. This explains why the error on the position determinedalgebraically is larger than when it is obtained statistically.

In a group of experiments involving the using the fluorescence techniquedescribed above, the signal reaching the photodetectors obeysessentially the 1/r model described in the previous section. However, anumber of important improvements had to be included.

First, it was found that attenuation of the light as it propagates bytotal internal reflection inside the glass needed to be taken intoaccount. Therefore a factor of exp(−αr) was included in the model. In a1.1-mm-thick sheet of Gorilla glass, we estimated the value of theattenuation coefficient to be α≈7 m⁻¹.

Second, we found that the response of the photodetectors dropped abruplybeyond 60° away from the normal direction. This was due to the design ofthe bezel, which included an O-ring in contact with the surface of theglass all along the edge in order to prevent stray light from hittingthe detectors. While it caused only negligible loss in the normaldirection, the O-ring caused significant attenuation for the lightentering the bezel at large angles. The angular dependence of thedetectors was accounted for by a super-gaussian transmission function ofthe form exp[−(θ/θ_(max))^(m)], with m an even integer. The valuesθ_(max)≈85° and m=6 were found to provide reasonable agreement with themeasured response profile.

Finally, the amount of scattered light is unknown and varies in time. Sothe model needs to include an overall unknown proportionality constantthat is allowed to vary from one time step to the next.

In addition, the sensitivity of the detectors can vary slightly from oneto the other. So the response of each detector needs to be multiplied bya known calibration factor, the value of which needs to be measured onceand is assumed to stay constant thereafter.

Gathering all these contributions, the response of the photodetectorscan be described by

$\begin{matrix}{{{f_{i}\left( {x,y,C} \right)} = {{CH}_{i}{g\left\lbrack {R_{i}\left( {x,y} \right)} \right\rbrack}{h\left\lbrack {\theta_{i}\left( {x,y} \right)} \right\rbrack}}},{where}} & (48) \\{{{g(R)} = \frac{^{{- \alpha}\; R}}{R}},} & (49) \\{{h(\theta)} = ^{- {({\theta/\theta_{\max}})}^{m}}} & (50)\end{matrix}$

and H_(i) denotes the calibration constant. This model contains threeunknowns parameters: the position (x,y) and the amplitude C. Although itis separable in R and θ, there is no requirement that it be that way.The distance is given as usual by

R _(i)=√{square root over ((x−x ₁)²+(y−y _(i))²)}{square root over ((x−x₁)²+(y−y _(i))²)}.  (51)

The angle can be obtained by taking the vector product between theposition vector and the normal to the edge of the sensor:

R _(i) ×n=zR _(i) sin θ_(i).  (52)

Calculating the vector product, we find that

$\begin{matrix}{{\theta_{i} = {\arcsin \; u_{i}}},{where}} & (53) \\{{u_{i} = \frac{{n_{iy}\left( {x - x_{i}} \right)} - {n_{ix}\left( {y - y_{i}} \right)}}{R_{i}}},} & (54)\end{matrix}$

and where n_(ix) and n_(iy) are the x- and y-components of the normalvector associated with detector i.

The calculation of the matrices α and β required for the chi-squareminimization algorithm require that we calculate the derivatives off_(i) with respect to its variable parameters. The derivative withrespect to the amplitude C is straightforward:

$\begin{matrix}{\frac{\partial f_{i}}{\partial C} = {H_{i}{g\left( R_{i} \right)}{{h\left( \theta_{i} \right)}.}}} & (55)\end{matrix}$

Those with respect to the position variables are

$\begin{matrix}{{\frac{\partial f_{i}}{\partial x} = {{CH}_{i}\left\lbrack {{{h\left( \theta_{i} \right)}\frac{\partial{g\left( R_{i} \right)}}{\partial x}} + {{g\left( R_{i} \right)}\frac{{h\left( \theta_{i} \right)}}{\theta}\frac{\partial\theta_{i}}{\partial x}}} \right\rbrack}},{with}} & (56) \\{{\frac{\partial{g\left( R_{i} \right)}}{\partial x} = {{- {g\left( R_{i} \right)}}\frac{\left( {x - x_{i}} \right)}{R_{i}^{2}}\left( {1 + {\alpha \; R_{i}}} \right)}},} & (57) \\{{\frac{{h\left( \theta_{i} \right)}}{\theta} = {{- m}\frac{\theta^{m - 1}}{\theta_{\max}^{m}}{h\left( \theta_{i} \right)}}}{and}} & (58) \\{\frac{\partial\theta_{i}}{\partial x} = {{\frac{- 1}{R_{i}\sqrt{1 - u_{i}^{2}}}\left\lbrack {\frac{u_{i}\left( {x - x_{i}} \right)}{R_{i}} - n_{iy}} \right\rbrack}.}} & (59)\end{matrix}$

The derivatives with respect to y are similar, except for ∂θ_(i)/∂y,which contains a sign difference:

$\begin{matrix}{\frac{\partial\theta_{i}}{\partial y} = {{\frac{- 1}{R_{i}\sqrt{1 - u_{i}^{2}}}\left\lbrack {\frac{u_{i}\left( {y - y_{i}} \right)}{R_{i}} + n_{ix}} \right\rbrack}.}} & (60)\end{matrix}$

The matrices α and β are then formed according to Eqs. (18) and (20) andfollowing the procedure illustrated in section 3. It is worth notingthat α is now a 3×3 matrix since there are 3 unknowns to solve for.

The position-detection algorithm described above is only one aspect ofthe program that manages the operation of the touch sensor. That programacquires the data generated by the controller board, checks for errors,performs data smoothing operations, monitors and updates the baselinelevel, calls the position-detection algorithm, decides whether theresult passes quality tests, manages the history of the touch eventsentered by the user and displays the results on the screen. In thissection we describe these tasks in more detail.

In our demonstration setup, the electrical signals generated by thephotodiodes are processed by a controller board. Among its manyfunctions, this controller generates the modulation signal that is usedto drive the infrared backlight. The modulation, around 1 kHz, isrequired in order to eliminate the ambient light. The controller boardreceives the 10 signals from the photodiodes, amplifies each of them andperforms synchronous detection by multiplying them by the modulationsignal and integrating over many periods. Then it discretizes eachchannel using an analog-to-digital converter and sends the resultthrough the serial port. This is the data stream that our Matlab programreceives as an input.

The data is first smoothed to reduce the noise. Without this step, thenoise is sufficiently large to cause jitter in the calculated position.The recursive time-domain filter used to smooth the data will bedescribed in the next section.

When the program is started, the signal level is monitored for a shortperiod of time (0.1 s) to acquire the baseline. This baseline issubtracted from the data and the result is the value that is passed tothe position-detection algorithm. The baseline is updated frequently asthe background level tends to drift, in particular due to dirt andfingerprints that accumulate over the surface of the touch screen. Thebaseline is adjusted so that it never exceeds the signal level and alsowhenever all signals remain constant for a sufficiently long period oftime (typically, 0.5 s).

The position-detection algorithm is called as soon as one of the signalsexceeds a certain threshold. How to pick the initial guess is andelicate issue as it can determine whether the algorithm converges ornot. When the algorithm is called for the first time, many positions aretried successively and the result that best fits the data is retained.The initial guess for the signal amplitude is estimated using the signallevels. When the algorithm is called subsequently, the results from theprevious time step are used as the initial guess for the next time step.

After a position is returned by the algorithm, it must pass a number ofquality tests. First, the signal amplitude (the parameter C) must beabove a certain threshold. This is necessary in order to identify theend of a touch event. Second, the uncertainty on the position (in termsof the standard deviations σ_(x) and σ_(y)) must be below a certainvalue. This ensures that only positions that have been determined withreasonable confidence are retained. Third, a data point is rejected ifit “jumps” too far from the previous value. This prevents unphysicallyfast displacements that tend to occur at the beginning and end of atouch event, when the signals increase from or decrease to weak values.

Finally, the program keeps track of the history of the session.Continuous traces are identified as such and displayed as continuouslines on the screen. A rudimentary “Paint” program allows users to seeon the screen what they draw on the surface of the glass.

It was mentioned previously that the signals coming from the controllerboard is smoothed before being fed to the position-finding algorithm inorder to reduce the jitter due to the noise. This step is carried out inthe time domain using a recursive linear filter (also called “infiniteimpulse response filter”). In this section we give an overview of thetheory for completeness.

Suppose that we have a stream of noisy data from which we want toconstruct a smoothed version in real time, as soon as the data becomesavailable. The information that is available is the set of all noisy andsmoothed values that have become available so far. The process used toconstruct the smoothed data is described by the general linear filter

$\begin{matrix}{{y_{n} = {{\sum\limits_{k = 0}^{M}{c_{k}x_{n - k}}} + {\sum\limits_{j = 0}^{N - 1}{d_{j}y_{n - j - 1}}}}},} & (61)\end{matrix}$

where x_(n) denotes the original, noisy data and y_(n) is the smootheddata. The goal is to determine the values of the coefficients c_(k) andd_(j) that will produce the desired filter. We relate this time-domainprocess to a filter defined in the frequency domain using a harmonicsignal as the input and making sure that the output satisfies thedesired filter. We assume harmonic signals,

x_(k)=x₀e^(2πikfΔ)  (62)

y_(k)=y₀e^(2πikfΔ),  (63)

with amplitudes x₀ and y₀ and period 1/f. Here, Δ denotes the samplingrate. Substituting into (61), we find a relationship between thecoefficients c_(k) and d_(j) and the desired filter function, H(f):

$\begin{matrix}{{H(f)} = {\frac{y_{0}}{x_{0}} = {\frac{\sum\limits_{k = 0}^{M}{c_{k}^{{- 2}\pi \; \; f\; \Delta \; k}}}{1 - {\sum\limits_{j = 0}^{N - 1}{d_{j}^{{- 2}\pi \; \; f\; \Delta \; {({j + 1})}}}}}.}}} & (64)\end{matrix}$

It is convenient to introduce z=e^(2πifΔ). Then the filter can berewritten as

$\begin{matrix}{{H(f)} = {\frac{y_{0}}{x_{0}} = {\frac{\sum\limits_{k = 0}^{M}{c_{k}z^{- k}}}{1 - {\sum\limits_{j = 0}^{N - 1}{d_{j}z^{- {({j + 1})}}}}}.}}} & (65)\end{matrix}$

If all d_(j)'s are zero, then the filter is non-recursive as it does notdepend on previous values of the smoothed data. Such filters are alwaysstable. If at least one d_(j) is non-zero, then the filter is recursive.Typically, recursive filters perform better, but they can be unstable.The condition of stability is that all roots of the characteristicequation

$\begin{matrix}{{z_{n} - {\sum\limits_{j = 0}^{N - 1}{d_{j}z^{N - j - 1}}}} = 0} & (66)\end{matrix}$

must lie in the unit circle.

A procedure to construct a filter that has the desired filter functionand at the same time satisfies the stability condition is outlined laterin this description. The idea is to use a change of variables that makesit easy to identify whether a filter function is stable or not. To thisend, we introduce

$\begin{matrix}{{w \equiv {\tan \left( {\pi \; f\; \Delta} \right)}} = {\frac{^{{\pi}\; f\; \Delta} - ^{{- }\; \pi \; f\; \Delta}}{\left( {^{{\pi}\; f\; \Delta} - ^{{- }\; \pi \; f\; \Delta}} \right)} = {{\left( \frac{1 - z}{1 + z} \right)}.}}} & (67)\end{matrix}$

This change of variables maps the inside of the unit circle (the regionof stability) to the upper half complex plane. So, in terms of w, thezeros of the characteric equation (66) must lie in the upper half planeto ensure stability.

As an example, consider the following: A simple low-pass filter is

$\begin{matrix}{{{{H(f)}}^{2} = \frac{b^{2}}{w^{2} + b^{2}}},} & (68)\end{matrix}$

where b is related to the cut-off frequency. Then the amplitude of theresponse is

$\begin{matrix}{{{H(f)}} = {\frac{b}{\sqrt{w^{2} + b^{2}}}.}} & (69)\end{matrix}$

To determine where are the poles of H are, we simply factorize thedenominator of the filter function:

$\begin{matrix}{{{H(f)}}^{2} = {\frac{b^{2}}{\left( {w + {ib}} \right)\left( {w - {ib}} \right)}.}} & (70)\end{matrix}$

The poles of H are at ±ib, but as we know by now, only +ib correspondsto a stable filter. So we keep only that factor in the expression forH(f):

$\begin{matrix}{{H(f)} = {\frac{- {ib}}{w - {ib}}.}} & (71)\end{matrix}$

One can verify that this expression satisfies the amplitude given by Eq.(69). The factor of −i was included to obtain the desired phase response(that is, zero phase shift at f=0). Using Eq. (67), the filter functioncan be written in terms of powers of z⁻¹:

$\begin{matrix}{{H(f)} = {\frac{\frac{b}{1 + b} + {\left( \frac{b}{1 + b} \right)z^{- 1}}}{1 - {\left( \frac{1 - b}{1 + b} \right)z^{- 1}}}.}} & (72)\end{matrix}$

By comparing with the general expression of a recursive filter, Eq.(65), we can simply read off the filter coefficients:

$\begin{matrix}{c_{0} = \frac{b}{1 + b}} & (73) \\{c_{1} = \frac{b}{1 + b}} & (74) \\{d_{0} = {\frac{1 - b}{1 + b}.}} & (75)\end{matrix}$

This simple filter only goes back one time step.

The filter described so far is not a very good filter, as its cut-off isvery slow. A filter with a more abrupt cut-off is obtained by using aslightly more complicated filter function:

$\begin{matrix}{{{H(f)}}^{2} = {\frac{b^{4}}{w^{4} + b^{4}}.}} & (76)\end{matrix}$

Its amplitude response is

$\begin{matrix}{{{H(f)}} = {\frac{b}{\sqrt{w^{4} + b^{4}}}.}} & (77)\end{matrix}$

There are now four poles, located at e^(iπ/4)b, e^(3iπ/4)b, e^(5iπ/4)band e^(7iπ84)b. Only the first two are located in the upper half-planeand satisfy the stability condition, so they are the only factors thatwe keep:

$\begin{matrix}{{{H(f)} = \frac{^{{\; \varphi}\;}b^{2}}{\left( {w - ^{{\pi}/4}} \right)\left( {w - ^{3\; {\pi/4}}} \right)}},} & (78)\end{matrix}$

where φ is a phase factor that we later determine to be π. Substitutingfor z, the filter can be rewritten into the standard form of Eq. (65).After some tedious algebra, we find that the recursion coefficients are

$\begin{matrix}{c_{0} = \frac{b^{2}}{b^{2} + {\sqrt{2}b} + 1}} & (79) \\{c_{1} = \frac{2b^{2}}{b^{2} + {\sqrt{2}b} + 1}} & (80) \\{c_{2} = \frac{b^{2}}{b^{2} = {{\sqrt{2}b} + 1}}} & (81) \\{d_{0} = \frac{2\left( {1 - b^{2}} \right)}{b^{2} + {\sqrt{2}b} + 1}} & (82) \\{d_{1} = {\frac{- \left( {b^{2} - {\sqrt{2}b} + 1} \right)}{b^{2} + {\sqrt{2}b} + 1}.}} & (83)\end{matrix}$

This filter goes back two time steps. Because of its sharper cut-off,this filter is the one that is implemented in the LightTouch prototype.We find that using a cut-off parameter b=03 gives adequate noisereduction.

Example Code Modulation Implementation

As discussed above, the driver circuit 144 may modulate one or more ofthe sources 110 such that the respective light therefrom includes acertain code or codes, such as orthogonal codes, like well known Walshcodes. For the purposes of discussion, this section provides a detaileddescription of an implementation of a modulator and demodulator circuitsuitable for carrying out code modulation to eliminate cross-talkbetween four simultaneous sources of light energy from the sources 110.

With reference to FIG. 9, a block diagram of a circuit is illustrated,which is suitable for providing the aforementioned code modulation anddemodulation. Notably, the same general circuit topology may be used toimplement any of the modulation embodiments discussed above (includingfrequency modulation), although there would be some firmware changes andsoftware changes to implement different modulation schemes.

A single receiver channel is shown with a single LED source 110 forsimplicity, it being noted that multiple sources 110 would be employed.The circuit may be employed for both phase-sensitive detection andspecific pseudo-random codes. In phase-sensitive detection mode, themicroprocessor 142 generates a bipolar (+/−1) square wave burst on line142A to the driver circuit 144. The square wave frequency is somewhatarbitrary, although it should be high enough to be above the 1/f noiseof the preamplifier 150 but low enough to be within the bandwidthlimitations of most low-cost, low-noise operational amplifiers. Inaddition, the frequency of the square wave burst should not be at aharmonic of the 60 Hz power frequency. A frequency of about 1 kHz workswell. The number of cycles in the square wave burst depends on manyfactors, but in order to measure at a 50 Hz rate to comply withMicrosoft's Windows 7 standard, 20 cycles (corresponding to 20 ms) tocomplete the entire sequence works well. The source 110 is driven by thesame square wave burst waveform; however, the sources 110 are switchedon only during the positive half-cycle of the square wave.

The touch signal will be synchronous with the source 110 output,generating a square wave photocurrent in the light sensing element 116(such as a photodiode). The photocurrent is converted to a voltage bythe transimpedance preamplifier 150.

The pre-amplifier signal voltage output on line 152 is multiplied by abipolar code in the multiplier block 160 to produce a product of suchsignal (line 152) and the code on line 154. Once the code burst iscomplete, the microprocessor 142 commands the analog to digitalconverter 180 to sample and digitize the output of the integrator 170followed a command to reset the integrator 170 by closing the dumpswitch. The value of the multiplier block 160 is chosen such that for aconstant background signal, after multiplication by the bipolar code,one arrives at a bipolar output signal on line 156 and an integration ofthe bipolar background signal leads of exactly zero. This results insynchronous detection while suppressing background light. There arebenefits beyond background suppression. Synchronous detection acts likea narrowband filter centered at the square wave frequency and withbandwidth approximately equal to 1/T, where T is the length of thesquare wave burst or integration time. Making the integration timelonger reduces the detection bandwidth and with it the noise.

The digitized signals (line 156) from all of the light sensing elements116 are collected by the microprocessor 142, which then computes thetouch position using the algorithms discussed in detail above.

As an alternative to using a bipolar square wave burst signal as thecode, there are other interesting choices. In order to implement anoptical receiver that senses light from some sources 110 and not others,Walsh codes may be employed, a class of pseudo-noise codes (which areused in CDMA cell phone networks). Walsh codes are easily constructed inlengths that are a power of 2. For other lengths, such as a 20-bitsequence, one uses the rows of the well-known Hadamard matrices. One ofthe order 20 Hadamard matrices is listed below.

$\begin{matrix} + & - & - & - & - & + & - & - & - & - & + & + & - & - & + & + & - & + & + & - \\ - & + & - & - & - & - & + & - & - & - & + & + & + & - & - & - & + & - & + & + \\ - & - & + & - & - & - & - & + & - & - & - & + & + & + & - & + & - & + & - & + \\ - & - & - & + & - & - & - & - & + & - & - & - & + & + & + & + & + & + & - & - \\ - & - & - & - & + & - & - & - & - & + & + & - & - & + & + & - & + & + & - & + \\ - & + & + & + & + & + & - & - & - & - & - & + & - & - & + & + & + & - & - & + \\ + & - & + & + & + & - & + & - & - & - & + & - & + & - & - & + & + & + & - & - \\ + & + & - & + & + & - & - & + & - & - & - & + & - & + & - & - & + & + & + & - \\ + & + & + & - & + & - & - & - & + & - & - & - & + & - & + & - & - & + & + & + \\ + & + & + & + & - & - & - & - & - & + & + & - & - & + & - & + & - & - & + & + \\ - & - & + & + & - & + & - & + & + & - & + & - & - & - & - & - & + & + & + & + \\ - & - & - & + & + & - & + & - & + & + & - & + & - & - & - & + & - & + & + & + \\ + & - & - & - & + & + & - & + & - & + & - & - & + & - & - & + & + & - & + & + \\ + & + & - & - & - & + & + & - & + & - & - & - & - & + & - & + & + & + & - & + \\ - & + & + & - & - & - & + & + & - & + & - & - & - & - & + & + & + & + & + & - \\ - & + & - & - & + & - & - & + & + & - & + & - & - & - & - & + & - & - & - & - \\ + & - & + & - & - & - & - & - & + & + & - & + & - & - & - & - & + & - & - & - \\ - & + & - & + & - & + & - & - & - & + & - & - & + & - & - & - & - & + & - & - \\ - & - & + & - & + & + & + & - & - & - & - & - & - & + & - & - & - & - & + & - \\ + & - & - & + & - & - & + & + & - & - & - & - & - & - & + & - & - & - & - & + \end{matrix}\quad$

Each of the + and − signs represents the +1 and −1 values of the bipolarsequence. Note that the codes are balanced. That is, there are equalnumbers of 1s and −1s so that the sum of each row is zero. Thus, theintegration of a constant background will be zero just like theaforementioned square wave code. An important property of these Hadamardsequences is that they are orthogonal. Thus, multiplying two differentcodes term by term and summing the results gives a zero result. It isthis property that makes a receiver driven by one Hadamard codeinsensitive to signals modulated with a different Hadamard code.

Referring to the block diagram of FIG. 9, it is apparent that if we adda second source 110 modulated with the row 1 Hadamard code, while themultiplier 160 is driven by the row 2 code, then the output of theintegrator 170 is zero because the circuit performs the same operationas described above.

Although the embodiments herein have been described with reference toparticular aspects and features, it is to be understood that theseembodiments are merely illustrative of desired principles andapplications. It is therefore to be understood that numerousmodifications may be made to the illustrative embodiments and that otherarrangements may be devised without departing from the spirit and scopeof the appended claims.

1. A touch sensitive display, comprising: a display layer; a transparentlayer disposed over the display layer; at least one source directinglight to propagate into and/or through the transparent layer; at leastone light sensing element in communication with the transparent layerand operating to receive scattered light in response to an objecttouching a surface the transparent layer and disturbing the propagationof the light therethrough; and a control circuit including a processorreceiving signals from the at least one light sensing element indicativeof the scattered light, and computing one or more positions at which theobject touches the transparent layer.
 2. The touch sensitive display ofclaim 1, wherein: the at least one source is in communication with thetransparent layer such that the light is coupled into the transparentlayer and propagates in a guided mode; and the object touching thetransparent layer causes a discontinuity and disrupts the guided mode ofthe light, thereby producing the scattered light.
 3. The touch sensitivedisplay of claim 1, wherein: the at least one source includes at leastfirst and second sources in communication with one or more edges of thetransparent layer; and the light emanating from the respective first andsecond sources includes at least one distinguishing characteristic suchthat the processor is operable to distinguish certain of the signals tobe from scattered light produced in response to the first source, andcertain others of the signals to be from scattered light produced inresponse to the second source.
 4. The touch sensitive display of claim3, wherein the at least one distinguishing characteristic includes atleast one of: a differing wavelength of the light emanating from thefirst source as compared to the light emanating from the second source;a temporal component whereby the light emanates from the first source atdiffering times as compared to the light emanating from the secondsource; a modulation component whereby the light emanating from thefirst source is modulated with a first code and the light emanating fromthe second source is modulated with a second code; and a furthermodulation component whereby the light emanating from the first sourceis modulated with a first frequency and the light emanating from thesecond source is modulated with a second frequency.
 5. The touchsensitive display of claim 4, further comprising: at least a firstsource in communication with a first edge of the transparent layer andproducing light within a first range of wavelengths; and at least asecond source in communication with a second edge of the transparentlayer and producing light within a second range of wavelengths differingoutside the first range of wavelengths, wherein the processor computesthe one or more positions at which the object touches the transparentlayer based in part on distinguishing that certain of the signals areproduced in response to light within the first range of wavelengths froma particular one or more of the light sensing elements, and certainothers of the signals are produced in response to light within thesecond range of wavelengths from a particular one or more others of thelight sensing elements.
 6. The touch sensitive display of claim 5,further comprising low reflectance pigment disposed along an edge of thetransparent layer opposite the first edge, and along an edge of thetransparent layer opposite the second edge, thereby reducing lightreflections at one or more edges of the transparent layer.
 7. The touchsensitive display of claim 6, wherein: the first and second edges areopposite one another such that each such edge includes low reflectancepigment thereon; and a respective window through the low reflectancepigment is disposed adjacent the at least first and second sources suchthat the light therefrom is coupled into the transparent layer.
 8. Thetouch sensitive display of claim 7, further comprising: at least onefirst filter disposed between the at least first source and thetransparent layer, and operating to attenuate light substantiallyoutside the first range of wavelengths; and at least one second filterdisposed between the at least second source and the transparent layer,and operating to attenuate light substantially outside the second rangeof wavelengths.
 9. The touch sensitive display of claim 9, wherein atleast one of the first and second filters including an infrared filteroperating to attenuate light in a infrared range of wavelengths.
 10. Thetouch sensitive display of claim 4, wherein: the control circuitincludes a light source driving circuit operating to energize the atleast first and second sources in time sequence; and the processorcomputes the one or more positions at which the object touches thetransparent layer based in part on distinguishing that certain of thesignals are produced at certain times in response to light from aparticular one or more of the light sensing elements, and certain othersof the signals are produced at certain other times in response to lightfrom a particular one or more others of the light sensing elements. 11.The touch sensitive display of claim 10, wherein the at least first andsecond sources produce light only within a range of infraredwavelengths.
 12. The touch sensitive display of claim 4, wherein atleast one of: the control circuit includes a modulation circuitoperating to modulate the first and second sources such that therespective light therefrom includes the first and second codes; thefirst and second codes are orthogonal codes; the orthogonal codes areWalsh codes; and the processor computes the one or more positions atwhich the object touches the transparent layer based in part ondistinguishing that certain of the signals include the first code andare therefore produced in response to light from a particular one ormore of the light sensing elements, and certain others of the signalsinclude the second code and are therefore produced in response to lightfrom a particular one or more others of the light sensing elements. 13.The touch sensitive display of claim 4, wherein: the control circuitincludes a modulation circuit operating to modulate the first and secondsources such that the respective light therefrom includes the first andsecond frequencies; and the processor computes the one or more positionsat which the object touches the transparent layer based in part ondistinguishing that certain of the signals include the first frequencyand are therefore produced in response to light from a particular one ormore of the light sensing elements, and certain others of the signalsinclude the second frequency and are therefore produced in response tolight from a particular one or more others of the light sensingelements.
 14. The touch sensitive display of claim 1, wherein: the atleast one source is a backlighting element of the display layer and isin communication with the transparent layer such that the lightpropagates through the transparent layer in a direction perpendicular tothe surface thereof; and the object touching the transparent layercauses a discontinuity and causes some of the light to couple into thetransparent layer, thereby producing the scattered light.
 15. The touchsensitive display of claim 1, wherein: the object fluoresces in responseto incident light from touching the surface of the transparent layer;and fluorescent light from the object couples into the transparentlayer, thereby producing the scattered light.
 16. The touch sensitivedisplay of claim 15, wherein: the at least one source produces lightwithin a first range of wavelengths; the fluorescent light from theobject is at one or more wavelengths substantially outside the firstrange of wavelengths; and the control circuit operates to distinguishbetween the fluorescent light and the light propagating from the atleast one source at least in part by determining that the signalsproduced in response to the fluorescent light are caused by light energyoutside the first range of wavelengths.
 17. The touch sensitive displayof claim 1, further comprising a light suppressing mechanism operatingto reduce light reflections at one or more edges of the transparentlayer.
 18. The touch sensitive display of claim 17, wherein the lightsuppressing mechanism includes a low reflectance pigment disposed alongat least one edge of the transparent layer opposite the at least onesource.
 19. The touch sensitive display of claim 17, wherein the lightsuppressing mechanism includes a tapering thickness of the transparentlayer at an edge thereof opposite the at least one source.
 20. The touchsensitive display of claim 1, further comprising an active styluscontaining the at least one source.
 21. The touch sensitive display ofclaim 20, wherein the active stylus further includes a light diffusingelement to diffuse the light from the at least one source prior to thelight propagating into and/or through the transparent layer.
 22. Thetouch sensitive display of claim 20, wherein the active stylus furtherincludes a switch circuit operating to activate the at least one sourceonly when the stylus is in contact with the transparent layer.
 23. Amethod, comprising: disposing a transparent layer over a display layer;directing light to propagate into and/or through the transparent layer;measuring scattered light in response to an object touching a surfacethe transparent layer and disturbing the propagation of the lighttherethrough; and computing one or more positions at which the objecttouches the transparent layer based on signals obtained by the step ofmeasuring the scattered light.
 24. The method of claim 23, furthercomprising: coupling the light into the transparent layer such that thelight propagates therein in a guided mode; and disrupting the guidedmode of the light by touching the surface of the transparent layer. 25.The method of claim 23, further comprising: directing the light into thetransparent layer via at least first and second sources in communicationwith one or more edges of the transparent layer; including at least onedistinguishing characteristic in the light emanating from the respectivefirst and second sources; and distinguishing, based upon the at leastone distinguishing characteristic, that certain of the signals to befrom scattered light produced in response to the first source andmeasured at a particular one or more locations of the transparent layer,and certain others of the signals to be from scattered light produced inresponse to the second source and received from a particular one or moreothers locations of the transparent layer.
 26. The method of claim 25,wherein the at least one distinguishing characteristic includes at leastone of: a differing wavelength of the light emanating from the firstsource as compared to the light emanating from the second source; atemporal component whereby the light emanates from the first source atdiffering times as compared to the light emanating from the secondsource; a modulation component whereby the light emanating from thefirst source is modulated with a first code and the light emanating fromthe second source is modulated with a second code; and a furthermodulation component whereby the light emanating from the first sourceis modulated with a first frequency and the light emanating from thesecond source is modulated with a second frequency.